### All ACT Math Resources

## Example Questions

### Example Question #1 : Coordinate Geometry

What line goes through the points (1, 3) and (3, 6)?

**Possible Answers:**

–2x + 2y = 3

4x – 5y = 4

2x – 3y = 5

–3x + 2y = 3

3x + 5y = 2

**Correct answer:**

–3x + 2y = 3

If P_{1}(1, 3) and P_{2}(3, 6), then calculate the slope by m = rise/run = (y_{2} – y_{1})/(x_{2} – x_{1}) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

### Example Question #1 : How To Find The Equation Of A Line

What is the slope-intercept form of ?

**Possible Answers:**

**Correct answer:**

The slope intercept form states that . In order to convert the equation to the slope intercept form, isolate on the left side:

### Example Question #1 : Lines

A line is defined by the following equation:

What is the slope of that line?

**Possible Answers:**

**Correct answer:**

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

### Example Question #1 : Lines

If the coordinates (3, 14) and (*–*5, 15) are on the same line, what is the equation of the line?

**Possible Answers:**

**Correct answer:**

First solve for the slope of the line, m using y=mx+b

m = (y2 – y1) / (x2 – x1)

= (15 *–* 14) / (*–*5 *–*3)

= (1 )/( *–*8)

=*–*1/8

y = *–*(1/8)x + b

Now, choose one of the coordinates and solve for b:

14 = *–*(1/8)3 + b

14 = *–*3/8 + b

b = 14 + (3/8)

b = 14.375

y = *–*(1/8)x + 14.375

### Example Question #2 : Lines

What is the equation of a line that passes through coordinates and ?

**Possible Answers:**

**Correct answer:**

Our first step will be to determing the slope of the line that connects the given points.

Our slope will be . Using slope-intercept form, our equation will be . Use one of the give points in this equation to solve for the y-intercept. We will use .

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

This is our final answer.

### Example Question #1 : How To Find The Equation Of A Line

Which of the following equations does NOT represent a line?

**Possible Answers:**

**Correct answer:**

The answer is .

A line can only be represented in the form or , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

represents a parabola, not a line. Lines will never contain an term.

### Example Question #1 : How To Find The Equation Of A Line

Let y = 3*x* – 6.

At what point does the line above intersect the following:

**Possible Answers:**

They intersect at all points

(–3,–3)

(0,–1)

They do not intersect

(–5,6)

**Correct answer:**

They intersect at all points

If we rearrange the second equation it is the same as the first equation. They are the same line.

### Example Question #1 : How To Find The Equation Of A Line

Which of the following is the equation of a line between the points and ?

**Possible Answers:**

**Correct answer:**

Since you have y-intercept, this is very easy. You merely need to find the slope. Then you can use the form to find one version of the line.

The slope is:

Thus, for the points and , it is:

Thus, one form of our line is:

If you move the to the left side, you get:

, which is one of your options.

### Example Question #2 : How To Find The Equation Of A Line

What is an equation of the line going through points and ?

**Possible Answers:**

**Correct answer:**

If you have two points, you can always use the point-slope form of a line to find your equation. Recall that this is:

You first need to find the slope, though. Recall that this is:

For the points and , it is:

Thus, you can write the equation using either point:

Now, notice that one of the options is:

This is merely a multiple of the equation we found, so it is fine!

### Example Question #2 : How To Find The Equation Of A Line

Given the graph of the line below, find the equation of the line.

**Possible Answers:**

**Correct answer:**

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

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